The Quality of Corporate Credit Rating: an Empirical Investigation

Transcription

1 The Qualy of Corporate Cred Rating: an Empirical Investigation Koresh Galil Berglas School of Economics, Tel-Aviv Universy Center for Financial Studies, Goethe Universy of Frankfurt October 2003 Abstract The qualy of external cred ratings has scarcely been examined. The common thesis is that the rating firms need for reputation and competiveness in the rating industry force rating agencies to provide ratings that are efficient wh respect to the information available at the time of rating. However, there are several reasons for doubting this thesis. In this paper I use survival analysis to test the qualy of S&P corporate cred ratings in the years Using sample data from 2631 bonds, of which 238 defaulted by 2000, I provide evidence that ratings could be improved by using publicly available information and that some categorizations of ratings were not informative. The results also suggest that ratings as outlined in S&P methodology were not fully adjusted to business cycles. The methodological contribution of this paper is the introduction of proportional hazard models as the appropriate framework for parameterizing the inherent ratings information. Keywords: Cred Risk, Cred Rating, Corporate Bonds, Survival Analysis JEL classification: G10, G12, G14, G20 Ean Berglas School of Economics, Tel-Aviv Universy Ramat-Aviv, Tel-Aviv, Israel. (koresh@post.tau.ac.il). This paper is part of my PhD dissertation under the supervision of Oved Yosha and Simon Benninga. I would like to thank Hans Hvide, Thore Johnsen, Eugene Kandel, Jan Peter Krahnen, Nadia Linciano, Yona Rubinstein, Oded Sarig, Avi Wohl, Yaron Yechezkel and seminar participants at Tel-Aviv Universy, Goethe Universy of Frankfurt, Norwegian School of Economics and Business Administration, CREDIT 2002, ASSET 2002, and EFMA 2003 for their helpful comments. My thanks also go to the board of the capal division of the Federal Reserve for providing a database on corporate bonds. Considerable part of this research was supported by the European RTN Understanding Financial Archecture.

2 Introduction Cred ratings are extensively used by investors, regulators and debt issuers. Most corporate bonds in the US are only issued after evaluation by a major rating agency and in the majory of cases the rating process is iniated at the issuer s request. Ratings can serve to reduce information asymmetry. Issuers willing to dissolve some of the asymmetric information risk wh respect to their credworthiness and yet not wishing to disclose private information can use rating agencies as certifiers. In such a case, ratings are supposed to convey new information to investors. Ratings can also be used as regulatory licenses that do or do not convey any new information. Contracts and regulations that have to be based on cred risk measurements have to relate to an accepted risk measurement. In such cases, ratings do not necessarily convey new information to investors and rating agencies play the role of providers of regulatory licenses. There are several reasons for questioning the qualy of the rating agencies product. The first reason is the noisiness of the information revealed by oligopolostic certifiers. Partony (1999) claims that the growing success of rating firms is a result of higher dependence of regulators on ratings. Corporations that want their bonds to be purchased by regulated financial organizations must have them graded by one of the recognized rating firms. However the number of such firms is low due to the reputation needs and regulation by the Securies and Exchange Commission (SEC). Such barriers to entry on the one hand and the high demand by bond issuers and regulators on the other hand might have given the rating agencies excessive market power. Several theoretical studies deal wh the informational disclosure strategies of monopolistic certifiers. Admati & Pfleiderer (1986) show that a non-discriminating monopolistic seller of information is reluctant to invest in gathering information. Moreover, he will also tend to produce noisy information since the more accurate the information, the faster is reflected in the securies prices and therefore the less valuable is for the buyer. Lizzeri (1999) shows that a monopolistic 2

3 certifier does not reveal any information since wishes to attract even the lowest types of firms. In such a case any firm refusing to pay the certifier discloses s low qualy. Lizzeri also shows that competion among certifiers can lead to full information revelation. The second reason for questioning the qualy of cred rating is inconsistency due to human judgment and methodology of the rating process. Rating agencies have to assess default risks of tens of thousands of firms from hundreds of industries in dozens of countries. This job is done by numerous analysts working in separate teams. Grading the default risk of firms under such circumstances is subject to inconsistencies. The third reason for examining ratings qualy is self-selection in bond markets. If a firm has alternative funding sources, then might decide not to issue a new bond if the rating receives is low. However, when such a firm gets a rating better than expected, would tend to issue a new bond. Such self-selection may cause ratings of new bonds to be less informative. One other possible direction for questioning the informational revelation of ratings concerns the breadth of rating categories. Reducing the number of categories might create a suation where is still possible to differentiate between firms whin each category by using publicly available information. To illustrate, might be that, whin a cred rating category, firms wh higher leverage tend to have higher default risk. 1 Several studies try to investigate qualy of ratings wh respect to revelation of new information. 2 The common test in these studies is based on testing the significance of the reaction of investors to changes in ratings. Kliger and Sarig (2000), when focusing on a refinement of Moody's rating system in 1982, show that investors indeed reacted to changes in ratings as if they 1 In April 1982 Moody's refined s ratings by splting each of the categories Aa, A, Baa, Ba, B into three subcategories. The fact that such a spl was possible indicates that prior to the spl one could use information to grade the firms whin each category. Such a possibily for further differentiation might still exist. 2 Griffin and Sanvicente (1982), Holthausen and Leftwich (1985), Hand, Holthausen and Leftwich (1992). 3

4 revealed new information. 3 However, this test is conducted on one event that does not necessarily reflect the informational content of ratings in subsequent years. A few papers test the qualy of ratings wh respect to informational efficiency. These studies focus on the inconsistency question only by testing the consistency of ratings across industrial segments and geographical regions. Ammer & Packer (2000) show that in some years US financial firms got higher ratings compared to other firms wh similar annual default risks. 4 Cantor et al (2001) also test the possibily of inconsistency across several groups. 5 These studies do not attempt to test the existence of any inconsistency across narrower sectors and or wh respect to any firm specific variable such as size or leverage. Nor do they test the information revelation of cred ratings sub-categories. Therefore, there is a need for more in-depth examination of the qualy of ratings. In this paper I test the qualy of corporate cred ratings wh respect to default prediction. I test whether ratings efficiently incorporate the publicly available information at the time of rating, to what extent the rating classification is informative and whether rating classifications are consistent across industries. In such examination, I allow the rating to be informative and to convey new information to the market. However, I also test whether the rating agencies could have provided a better rating using the information available at the time of rating. This test goes beyond the empirical tests by Ammer & Packer (2000) and Cantor et al (2001) by testing the efficiency of ratings wh respect to other firm characteristics and narrower industrial classifications. 3 For this test Kliger and Sarig use the unique event of spl of Moody s ratings to subcategories in In this event, Moody s divided each of ratings Aa till B into three sub-categories such as Aa1, Aa2, Aa3 B1, B2, B3. This is a unique case in which the rating agency makes a change in rating which is not accompanied by any real economic change in the rated companies. 4 The test deals wh consistency across four groups only - US financial firms, US non-financial firms, Japanese financial firms and Japanese non-financial firms. 5 The research has been prepared for Moody's Investors Service and partially tests the consistency of Moody's ratings. The test was of consistency of rating across US firms and non-us firms, banks and nonbanks. Their results show that speculative grade US banks tend to have higher annual default rates compared to speculative US non-bank firms over the years A comparison of US and non-us speculative grade issuers over the years produced similar results - US firms had significantly higher annual default rates. However, allowing time-varying shocks to annual default rates made these differences between sectors statistically insignificant. 4

5 Cred risk is usually perceived in three different dimensions - probabily of default, expected default loss and cred qualy transion risk. In this study I review the methodology of the rating process used by Standard & Poor s (S&P) and show that the corporation's senior unsecured (issuer s) rating is an estimate of the firm's long-term probabily of defaulting. To represent this long-term default probabily I use the hazard rate - the probabily of default at time t condional on survival till time t. The empirical test is based on survival analysis using a proportional hazard model. This is the first study to use such a model to parameterize the cred rating and shows that is a more refined approach to addressing the meaning of rating as interpreted by the rating agencies announced guideline. This methodological innovation also enables the curse of rare events in empirical studies of defaults to be overcome, since views cases of defaults whin a long-term horizon and not whin an annual horizon. Therefore, this empirical method is an improvement wh respect to both addressing the real meaning of rating and overcoming the curse of rare events. Using partial maximum likelihood, is possible to test whether publicly available information concerning the issuer, as well as industrial and geographical classifications, is significant in explaining default hazard rate after controlling for rating. I also test to what extent the categorization in S&P rating is informative wh respect to default prediction. Or in other words, I test whether ratings could be based on less rating categories whout loss of relevant information. The database used in this study is que unique. A list of 10,000 new corporate bonds issued in the US during the years is linked wh the issuers characteristics retrieved from Compustat and lists of default occurrences during the years , obtained mainly from Moody s Investor Services publications. After eliminating financial corporations, multiple issues by single issuers whin a calendar year, and other observations wh key variables missing, a database wh 2631 bonds of 1033 issuers is left. The long-term horizon that features the survival analysis enables 238 cases of default by 158 firms to be identified. Therefore this 5

6 methodology enables hypotheses to be tested that could not be addressed using tradional methods. The results show that the S&P rating categorization during the sample period is not fully informative. The probabilies of default for two adjacent rating categories are not significantly different from each other. Moreover, the estimated probabilies of default do not follow the expected monotonic structure. This result is also supported by figures provided by S&P self. However, contrary to some claims, S&P ratings not only enable a distinction to be made between investment grade firms and speculative grade firms but also to some extent whin each of these two groups. Another main result is the inefficient incorporation of publicly available information in ratings. Firm characteristics such as size, leverage, and provision of collateral and industrial classification explain default probabily even after controlling for the informational content of ratings. The robustness tests show that using issuers ratings instead of issues ratings does not change these results. It is also shown that this addional explanatory power exists even when controlling for the full informational content of ratings (sub-categorized ratings). The paper also attempts to examine to some extent, whether the anomalies found are consistent during the sample period and hence applicable for improving ratings. When the sample is spl into two sub-samples and the estimation process repeated, appears that the provision of collateral and leverage still retain their addional explanatory power in the same direction in both sub-samples. However, the results concerning size of the firm and industrial classification do not follow a fully consistent pattern across the two sub-samples. Hence, this exercise indicates that the firm-specific information, such as provision of collateral and leverage, were not efficiently incorporated in the assignment of ratings. It cannot be ruled out that the explanatory power of industrial classification after controlling for rating is due to shocks that were correlated wh the classification only ex-post. 6

7 It is also shown that when testing the significance of publicly available information after controlling for informational content of ratings, the narrower the definion of industrial classification, the more significant the variables such as size and leverage. Or in other words, the more exact the controlling for industrial classification, the more significant the addional explanatory power of size and leverage. This pattern supports the thesis that rating agencies fail to correctly incorporate the heterogeneous interpretation of such variables across industries. The remainder of the paper is organized as follows. In Section I, I review the rating industry and rating process. Section II describes the methodology used. Section III describes the data and Section IV the results. Section V contains the conclusions. I. Rating industry and rating process The main bond rating agencies in the Uned States are Moody's Investors Service (Moody s) and Standard and Poor's (S&P). Since the mid-1980s there has been a tremendous increase in rating activy. 6 In the 1980s S&P and Moody's employed only few dozen whereas today they employ thousands. Moody's annual revenue reached $600 million in year 2000, of which more than 90% was derived from bond rating, and s total assets amounts to $300 million. Moody s financial results reveal high profabily wh annual net income in 2000 reaching $158 million (52.8% of s total assets). A rating, according to rating agencies definion, is an opinion on the credworthiness of an obligor wh respect to a particular debt. In other words, the rating is designed to measure the risk of a debtor defaulting on a debt. Both Moody s and S&P rate all public issues of corporate debt in excess of a certain amount ($50 million), wh or whout issuer's request. However, most 6 See Whe (2001) for details. 7

8 issuers (95%) request the rating. The rating fees are based on the size of the issue and not on any known characteristic of the issuer. These fees are relatively small compared to the size of issues. 7 When an issuer requests a rating for s issue, S&P assigns a special commtee and a lead analyst to assess the default risk of the issuer before assessing the default risk of the issue self. 8 The commtee meets the management for a review of key factors affecting the rating, including operating and financial plans and management policies. Following the review, the rating commtee meets again and discusses the analyst's recommendation. The commtee votes on the recommendation and the issuer is notified of the decision and the major considerations. The S&P rating can be appealed prior to publication if meaningful addional information is presented by the issuer. The rating is published unless the company has publication rights, such as in a private placement. All public ratings are monored on an ongoing basis. It is common to schedule an annual review wh management. Ratings are often changed. The main factors considered in assigning a rating are: industry risk (e.g. each industry has an upper lim rating no issuer can have a higher rating regardless of how conservative s financial posture); size - usually provides a measure of diversification and market power; management skills; profabily; capal structure; cash flow and others. For foreign companies, the aggregate risk of the country is also considered. In particular, foreign companies are usually assigned a lower rating than their governments - the most credworthy enty in a country. S&P uses ten rating categories, AAA to D while Moody's uses nine categories, from Aaa to C. Both agencies divide each of the categories from AA (Aa) to B into three subcategories; e.g. AA category (Aa of Moody s) is divided into three subcategories AA+ (Aa3), AA (Aa2) and AA- (Aa1). Portfolio managers are required by regulators or executives not to hold 'speculative bonds'. It is common practice to use cred ratings to define such bonds. Bonds wh rating 'BBB' 7 S&P charges amounts of $25,000 up to $125,000 on issues up to $500 million and up to $200,000 on issues above $500 million. Rates are negotiable for frequent issuers. 8 Since the empirical test is based on S&P ratings, the methodology presented is of S&P. Moody's rating methodology is que similar. 8

9 or 'Baa' and higher are called 'investment bonds' and bonds wh lower ratings are called 'speculative bonds' or 'junk bonds'. Therefore, from the perspective of some bond issuer, reaching grade of 'BBB' or 'Baa' is a crucial minimum. After assigning a rating to the issuer, the rating agency assigns ratings to s issues on the same scale. The practice of differentiating issues of the same issuer is known as notching. Notching takes into account the degree of confidence wh respect to recovery in case of default. The main factors considered at this stage are seniory of the debt and collateral. Notching would be more significant the higher the probabily of default of the issuer. For example, a very well secured bond will be rated one notch (subcategory) above a corporate rating for investment grade categories and two notches in the case of speculative grade categories. One important fact about rating is that neher the issue s rating nor the issuer s rating changes over time unless a fundamental change has occurred to the likelihood of payment by the company. Therefore, rating cannot be interpreted as being simple prediction of default. Otherwise the shorter the time to matury of a bond, the higher s rating would be. Because ratings do not change, as the bond gets closer to s matury date, is reasonable to assume that a rating is an estimate of a company's specific default risk, regardless of the time horizon. Survival lerature offers a suable framework for analysis as focuses on the determinants of a 'hazard rate' - the probabily of default of the company at time t condional on survival until till time t. If hazard rate is constant over time, the rating can be interpreted as being an estimate of this rate. In a more general case, where hazard rate is not constant, the rating can be interpreted as an estimate of a company's inherent default risk (that affects s hazard rate for any time horizon time t ). 9

10 II. Methodology A. Framework Many firms issue bonds annually and some even issue multiple bonds concurrently. Let t denote one of these times in which a firm i issues a new bond. At this time the rating agency examines the credworthiness of the firm and assigns a grade G to the firm. This rating is intended to indicate the general risk of firm i defaulting on any type of debt at anytime in the future. This rating is based on all information available at time t irrespective of the characteristics of the bond self (especially ignoring the time to matury). Then the rating agency examines the protections offered to the new bondholders and carries out notching (as described in section I). If the bond is very well secured may get a rating B G, that is 1-2 grades (in subcategory terms) better than that assigned to the firm self - G. And if is subordinated may get a rating B G which is 1-2 grades lower than that assigned to the firm. G B is also independent of other characteristics of the bond such as time to matury, rate of coupon, size of issue and others. For the purpose of testing qualy of rating wh respect to default probabily, would be best to have a dataset and a methodology based on firms ratings. However, since the data on firms ratings is not complete and might cause problems of self-selection, the methodology is tailored for a database on issues ratings (bonds ratings). To do this, I first describe the nature, i.e. the stochastic default process, and then I describe how issuers ratings and issues ratings relate to the fundamentals of this process. Then I show how, whin this framework, is possible to use the available database to test the qualy of ratings. 10

11 B. Distribution of Default Occurrence Assume that all firms that are exposed to default risk experience default at some time in the future, or in other words, default is just a matter of time. This assumption does not contradict historical experience. Firms wh the highest ratings (AAA) have deteriorated over time to D default. Let T be the time from t till the first time the firm i defaults. 9 Suppose the time T has a continuous probabily densy f ( T; x, t) where T is a D realization of D T and x is a vector of characteristics of firm i at the time of rating t. The probabily distribution of D T for a single firm i may change over time because of several reasons. First, the firm s characteristics x may change over time and hence cause a change in the probabily distribution. 10 Second, a change in probabily distribution can also occur due to macroeconomic factors, and therefore a firm wh the same characteristics x = xi t 1 may have different probabily distributions at times t and t 1. The cumulative probabily of D T is: D F( T; x,) t = Pr( T T) = f(; s x,) t ds, (1) T 0 The survival probabily function is: D F( T; x, t) = Pr( T > T) = 1 F( T; x, t). (2) The hazard rate, θ ( T; x, t), is the probabily that default occurs at time T, given that had not occurred before T : 9 A firm defaults if is not able to pay interest or par of any outstanding bond. When a firms defaults on one bond, does so on all s outstanding bonds. Therefore, any outstanding bond at time t defaults if and D only if s time to matury is greater than T. 10 In fact, only unexpected changes of firm s characteristics can change the probabily distribution, since any affect of expected change in x is already incorporated in the probabily distribution of T at time t. 11

12 θ, f and f ( T; x, t) θ ( T; x, t) =. (3) F( T; x, t) F are alternative ways of describing the same probabily distribution of default. However, is common to use θ to describe the distribution. The hazard rate may have a term structure over T. It can be argued that ceterus paribus the hazard rate five years after issuing the new bond has to be different from that in the year following the new issue. For example, the flow of cash into the firm may cause s hazard rate to be low in the first years following the new issue and then to increase when the cash runs out. In such a case, the hazard rate should have an increasing pattern over time T, possibly converging to some upper bound. Following this argument, if the firm issues new bonds from time to time, one can expect the hazard rate to increase over time and then decrease whenever new debt is issued. Yet, is also possible to rationalize decreasing hazard rate. For example, if a firm gains a posive reputation merely by surviving, which translates into lower probabily. The historical evidence of the average hazard rate s term structure reveals that first increases over time and then decreases. Moreover, appears that the term structure of the average hazard rate depends on the level of default risk self; the riskier the issuer/issue (the lower s rating), the faster s hazard rate reaches the maximum and starts to decrease. However cannot be ruled out that these results are due to the unobserved heterogeney that exists in each rating category. Moreover, when assigning a rating to a firm, rating agencies assure that s rating will not change unless there is a fundamental change in the firm s profile. Combining the fact that the assigned rating has no time horizon perspective (except, that is, long term), can be concluded that the rating agencies ignore the term structure of the hazard rate and hence they also ignore the possibily that this term structure depends on the level of default risk. For a more detailed examination of this issue (historical evidence of hazard rate term structure) see Appendix A. 12

13 C. Proportional Hazard Rate For a constant hazard rate, the hazard function is denoted θ ( T ; x, t ) = k ( x, t ) and the survival probabily function is FT ( ; x, t) = e k( x, t) T which is the exponential distribution function. The hazard rate may change monotonically over time. Such a 1 a case can be represented by the Weibull distribution wh θ ( T ; x, t ) = k ( x, t ) a T as the hazard rate function. If a > 1, then θ is increasing over time, and If 0< a < 1 is decreasing over time. If a = 1 the hazard function is constant over time and the Weibull distribution has an exponential form. Both the exponential and Weibull distributions, as well as most of the common distributions used in survival analysis, are special cases of the proportional hazard distribution, for which the hazard rate is of the form θ ( T; x, t) = k( x, t) k2 ( T). For the exponential distribution k 2 ( T ) = 1, and for the Weibull distribution ( ) a k2 T 1 = at. This structure assumes that the hazard rate function is separable i.e. the term structure of the hazard rate k ( T) 2 is uncondional on the firm s specific component kx (, t). Cox (1972) points out that is possible to estimate the parameters of kx (, t) whout specifying the form of the baseline hazard function k ( T) 2 and therefore, this structure is very helpful. The proportional hazard rate sus the objectives of this test and the Cox nonparametric approach is adopted for the estimation process. D. Rating Process each time t. It is assumed that the rating agency provides an estimate of k k( x, t) for each firm i at 11 After estimating k the rating agency publishes a grade G on a scale of 1 to n using the following algorhm, 11 According to S&P methodology, ratings are not fully adjusted to business cycles. Therefore the definion of the target parameter for rating agencies should have been kx (, ). However assuming that the 13

14 G 1 if lnk c1 2 if c1 < lnk c2 =.. n if cn 1 < ln k, (4) where k is the rating agency's estimate for and C = ( c, c,..., ) is a set of n 1 cutoff points k 1 2 cn 1 chosen by the rating agency. G is a rating assigned to the firm self. Then a rating B G is assigned to the new bond issued by the firm. When assigning a rating to a new bond, the rating agency also considers collaterals provided for the bond self, which cause the expected default B loss of the bondholders to decrease should default occur. Therefore, G = G +notch( collateral) where notch(. ) { 0, 1,1, 2, 2} is the function that represents the notching process as described in section I. We may question whether the rating G is a sufficient statistic for k condional on the information x and time t. If not, a better estimate for k can be achieved by combining G and x. This does not mean that a better estimate can be achieved by using publicly available information only, as rating agencies can also rely on information that is not publicly available. In such a case, using publicly available information only would not necessarily lead to a better estimate of k. The objective of this paper is to test whether a combination of rating G, or in fact B G as a proxy for G, wh publicly available data could improve the estimate for k. E. Estimation The estimation follows survival analysis. In such a framework, the hazard rate of default or equivalently the time to default D T is the dependent variable. First, the hazard function has to rating agency tries to estimate kx (, t). kx (, t) enables us to test S&P s claims by estimating the parameters of t in 14

15 be described. As mentioned above, the hazard function is assumed to be proportional - θ ( T; x, t) = k( x, t) k ( T). The firm's specific default risk component k = k( x, t) is formed as 2 follows, ln k = g ' βg + SECURED βsecured + x ' βx + τ ' βτ (5) B G and t which are discrete variables are transformed into sets of dummy variables. Formally, g = ( g, ) where 1, g2,,, gn 1, g = 1 if G B = j and g = 0 otherwise and j, j, τ τ τ τ = ( 1, 2,..., H 1) where τ h = 1 if t h = and τ = 0 otherwise ( H is the total number of years that h new ratings were released in the sample). 12 SECURE D is a dummy variable that indicates whether the bond whose rating is used for the observation was secured by a collateral. In such a case G B G and therefore, to calculate the default hazard risk, the affects of notching should be deducted by adding the variable SECURED. However, providing collateral might also serve as a signal for the firm s qualy as described in Bester (1985). Hence, this dummy variable can be a control for both the notching effect and the signaling. x is a vector of firm's specific variables at the time of rating assignment. β, β, g x β secured and β τ are vectors of the corresponding parameters. It is not necessary to determine a source of noise in this equation because the left hand side variable of this equation determines the probabily distribution self. k is assumed to be deterministic. Let T be the continuous period the firm i is observed in the sample to have been exposed to default risk since the issue of the new bond at time t. The end of each period T can be caused eher by default or censorship. Censorship occurs if D T is not realized (no default has 12 B For example if G {1, 2, 3}, then for G = 3 g = ( 0 0 1). B B 1 B G = g = ( 1 0 0), for G 2 = g = (0 1 0 ) and for 15

16 occurred during the period T ). In other words, an observation is censored if D T < T and uncensored if T = T D. Then, for each observation can be defined, s 1 = 0 if default D ( T = T ) D ( < ) if censorship T T. (6) Note that each observation is of one S&P rating g assigned to the first new bond issued j, by firm i at year t, the period T, and the characteristics of the firm at the time of rating - x. Since the empirical test is cross-sectional, for ease of notation would be simpler to denote each observation of the bond s rating of firm i at year t as an observation j, and the variables D T,T, x, s would be notated T D j, T j, x j and s j respectively. The estimation of equation (5) is possible by adopting the partial likelihood apprach as introduced by Cox (1972). Consider an uncensored observation wh the time to default T. The pratial lieklihood of this observation can be calculated by deviding s hazard rate to default at the end of period T by the sum of hazard rates at this point ( T ) of all firms that were exposed to default udring the whole period T. The construction of the partial likelihood PL j for observation j is as follows, θ ( Tj, xj, t) k( Tj) kj kj PLj = = = kt ( j ) Q θ ( T, x, v) Q k Q k = l Q l jl, j l jl, l jl, l l l exp( g ' β + SECURED β + x ' β + τ ' β ) j g j secured j x exp( g ' β + SECURED β + x ' β + ν ' β ) jl, l g l secured l x τ τ (7) where Q jl, = 1 if Tl T j and Q jl, = 0 otherwise (The Q s enable to include in the denominator, firms that were subject to default risk during T j ). Since the baseline hazard 16

17 function k ( T) 2 is equal for all firms, is canceled out from the calcualtion of the partial likelihood. The partial likelihood of the sample function can be formed: PL( β, β, β, β ) = g secured x τ m j i l = 1 exp( g j ' βg + SECUREDj βsec ured + x j ' βx + τ ' β ) τ Qjl, exp( gl' βg+ SECUREDl βsecured + xl' βx+ ν ' βτ ) s j (8) Note that the partial likelihood of the sample is the multiplication of the partial likelihood of the defaulted firms only ( s j = 1 ). However this partial likelihood is not biased since the likelihood for each uncensored observation PL j is s hazard rate to default relative to all other observations that were exposed to default risk during the period T j, whether censored observations or uncensored. Therefore, there is no problem of selection-bias wh this respect. This is one of the novelties of the method introduced by Cox (1972). Now equation (5) and s parameters β g, β x, β secured and β τ can be estimated using the Maximum Likelihood procedure. Clustering is used to correct the standard error estimates of the coefficients for bias that might be caused due to multiple observations of companies in different years. 17

18 III. Data A. Database The database for the study was created by combining data from three main sources. A list of more than 10,000 corporate bonds issued during the years was obtained from the Capal Division of Federal Reserve. 13 Each issue in this database is detailed wh name of issuer, date of issue, S&P and Moody's rating at date of issue and other characteristics of the bond. The financial statement data, SIC classification, country of incorporation and S&P unsecured senior debt ratings were obtained from Compustat. A list of default events was mainly obtained from Moody's Investor's Service publications. After combining all these sources and eliminating financial corporations, multiple issues whin each year, companies wh no S&P rating and companies that could not be linked to Compustat, 2631 bonds of 1033 non-financial corporations remained. Of which 238 bonds belong to 158 firms that default at some point after appearance of their issues in the sample. Many corporations issued more than one bond during the sample period. Using observations wh data on senior unsecured S&P rating would lim the database to 2487 issues (176 defaulted) of 861 companies (106 defaulted). Therefore being attached to direct issuer rating (senior unsecured rating) instead of issue s rating would not only significantly decrease the number of observations but also create a biased sample. This is due to the fact that the rate of defaulted companies wh no issuer rating is much higher than s proportion in population. Using issue's rating instead of issuer's rating imposes special considerations on the estimation, as is described in section II. 13 This dataset is used by Guedes & Opler (1996) and is in the public domain. 18

19 B. Data Definion First, T the time that firm i has been exposed to default risk since time t is calculated. This period depends not only on the time to matury of a bond issued at time t but also on bonds issued before and after time t. For example, if the time of matury of a bond issued at time t 1 is year 1999 and the time of matury of the bond issued at time t is 1998, then is clear that the firm has been exposed to default risk since t 1 through time t till Therefore, if a firm had two or more issues wh some overlapping period (from date of issue to date of matury), then the period of exposure to default risk for each observation at time t was calculated from t till the latest matury date. If the firm defaulted during this period then the final period T was calculated from s date of issue till date of default. In such a case (and only in such case) the observation is considered to be uncensored ( s = 1). For all observations, where the period of i exposure to default risk has not ended wh default, the observation is considered to be censored ( s = 0 ). An observation is also considered censored if the time of exposure to risk is beyond year i The reason for that is that is not known at what exact time (after year 2000) the firm defaults. For a thorough description of T and several examples see appendix B. Companies specific variables are chosen in accordance wh empirical bankruptcy prediction lerature. The variables are based on the first quarterly or annual financial statements published following the issue and do not rely on market data. Using data from financial statements prior to issue would ignore the changes that could occur due to the issue self, such as changes in leverage and total assets. Size appears to be the most significant variable in multivariate prediction of default. The bigger the firm, the more diversified s assets and therefore the lower s default risk. Size is calculated as ln( Total Assets) to enable diminishing return to scale in respect of diversification. Quick ratio ([Current Assets Inventories]/Current Liabilies) is a proxy for liquidy of the firm. The more liquid assets a firm has, the lower s propensy to default in the short term. 19

20 However survival analysis is based on measures of long term default propensy. Hence, is not clear whether this variable should be significant. Leverage is calculated as (Total Liabilies/Total Assets). The higher the leverage, the higher the firm s exposure to default risk and s propensy to default. Profabily is calculated as (EBIT/Total Assets). The more profable the firm, the more resources has to pay debtors, and the lower s propensy to default. Secured is a dummy variable that indicates whether the company could provide some kind of collateral for s bond (such as First Mortgage, Equipment Trust or other). Firms are also exposed to the macro-economic risks of their economies and this factor is also considered by rating agencies. The US economy is considered to be one of the most stable economies. Hence, a dummy variable was used to indicate whether the company was incorporated outside the US. Exposure to industrial risk, which is also considered in the rating process, is expressed by dummy variables indicating the industrial classification according to standardized industrial classification (SIC). The ratings observations are taken over 11 years ( ). Some firms appear in the sample several times since they issued new bonds in several different years, while other firms only appear in the sample once. Since rating is supposed to incorporate all relevant information at any time of observation, is possible to treat multiple observations of firms separately and test whether ratings are efficient at any time. Therefore even though the sample includes multiple observations on some firms, a cross section analysis is adopted. Yet, I use clustering to calculate the standard deviation of coefficients to correct the bias that might occur due to multiple observations of firms. Dummy variables are used for each of the years 1983 till 1992 (year 1993 is the benchmark). These dummy variables are proxies for the macroeconomic factors that affect default risks and they also solve other fundamental and econometric problems. There may be some correlation between some variables and the macroeconomic state. Suppose in 'bad years' only large Size firms issue new bonds. The correlation between Size and 'bad years' would cause 20

21 biased estimators for Size and misinterpretation of the results. Rating categorization may also have changed during the sample period. 14 Using these dummy variables for year of issue can answer these two possible cases. C. Data Description Table I shows the distribution of the sample across main rating categories and observation of default. As can be seen, 851 (32.3%) of the bonds were speculative graded and 193 of those speculative bonds belonged to firms that defaulted later. Out of the 238 default observations, 193 (81.1%) belonged to firms that issued speculative bonds. The high rate of speculative bonds, as well as the adoption of the hazard model structure leads to the result of 9 percent of defaults among the bond observations and 15.3 percent among the firms. These high default rates in the sample enable investigation of the default stochastic process. It can also be seen that the lower the rating the higher the rate of defaults. In this respect, the sample seems to answer the expectations. The rate of bonds graded BB is que small. This may be a result of self-selection, i.e. firms which were graded very close to investment grade might wa for a better time for issuing a new bond or seek cheaper sources of funding. Another explanation might be a rating agency s interest not to grade companies close to the hedge to avoid a bad taste. 15 The distribution of the issuers shows the same patterns as the distribution of the bonds. Insert Table I about here 14 See Blume, Lim & Mackinlay (1998). 15 A parallel example of such consideration is grading in schools. Do teachers avoid failure grades that are too close to pass? 21

22 Table II shows the distribution of the sample across rating subcategories. As can be seen, each rating category which is subcategorized is indeed que spread across s subcategories and the sample includes cases of default whin each sub-category. Insert Table II about here Table III describes the one-dig Standardized Industrial Classification (one dig SIC) of the sample. These industrial groups are que large and each includes many cases of default. However great heterogeney can be expected in each of these groups wh respect to default risk. Therefore the statistical tests will also try to address narrower industrial classification. Insert Table III about here Table IV shows the industrial classification of the sample when the industries Manufacturing & Equipment and Public utilies are sub classified using two-dig SIC. Table V-a shows a more refined industrial classification using two-dig SIC. Each industrial classification consists of at least 15 firms and 19 observations (bonds). All other industries that have not reached these numbers are gathered in a group called other. Table V-b describes the industrial classifications of these industries. The rate of cases of default in this group (19.5 percent of the bonds and 26.3 percent of the firms) is greater than that of the sample (9.0 percent of the bonds and 15.3 percent of the firms). These numbers indicate that the default risk of this group is greater than that of the whole sample. Insert Tables IV-V about here 22

23 Table VI shows the classification of country of incorporation. 49 bonds of 24 firms belong to firms incorporated outside of the US. Each of these countries only has a small number of bonds and firms. Therefore, for the purpose of this study, they were all gathered in one group Incorporated out of US. However, the distribution of the firms and bonds across countries does not seem to be representative of the population. Therefore, a dummy variable is included in the regression for incorporation outside the US merely for controlling purposes, but not for testing the inconsistency of ratings across countries. Insert Tables VI about here IV. Results A. Estimation of hazard function Table VII shows the results of three runs for estimation of the hazard function of companies wh regard to S&P bond ratings on main-categories scale and one-dig industrial classification. In the first run, hazard function is estimated whout using rating classifications. As expected, smaller Size, higher Leverage, lower Profabily, Incorporation out of the US and lower Liquidy increase companies' tendency to default. As expected Liquidy' s effect is insignificant. The significant negative coefficient of the dummy variable Secured indicates that provision of collateral indeed signals lower tendency to default. Analysis of industrial classification reveals that during the sample period some industries were significantly 'safer' than the others Manufacturing, and Public Utilies. 16 Mining & Construction, and Wholesale & Retail were significantly riskier than other companies. Coefficients of cohort dummies show that issues from the 80's were subject to higher default risk compared wh those issued in 90's. 16 Note that the significance of the Industrial classification dummies depends on the composion of the benchmark (the omted dummy variable for industrial classification) in this case the services industry. Table III reveals that a larger fraction of this industry has experienced default compared to the whole population. 23

24 Insert Table VII about here In the second run, hazard function is estimated using S&P ratings on main-categories scale and cohort dummies for year of issue. The results show that in general the higher the rating, the lower the default risk. Coefficients of rating classifications express two anomalies. First and as reflected in figure 1, they are not fully monotonic. The coefficient of AA is expected to be smaller than that of A, yet appears to be larger. Insert Figure 1 about here Furthermore, the difference between most adjacent ratings is insignificant. Table VIII shows the t statistics for the differences between the rating coefficients as estimated in the second run. It appears that ratings AAA, AA and A are not significantly different from each other. However rating A is significantly different from rating BBB. It could be claimed that this is the result of the low number of default cases in each category. Yet, this should not have brought about the non-monotonic behavior of the point estimates. The results concerning the subcategorized ratings shown later support this non-monotonic and non-significant behavior of the ratings. However one interesting result is that ratings have at least some distinguishing power whin each group of investment grades and speculative grades. Rating A is significantly better than rating BBB even though they are both investment grades, and rating BB is significantly better than B even though they are both speculative grades. Insert Table VIII about here The third run (table VII) shows the results of estimation of a hazard function considering rating information as well as firm-specific characteristics, industrial classification and cohort 24

25 dummies. If rating is consistent across industries and countries, if correctly incorporates all the specific characteristics of firms and if the rating categories are narrow enough, should be expected that all the coefficients, except those of ratings dummies and Secured, are zero. Since a bond s rating is raised when is secured, the coefficient of Secured is supposed to be posive. 17 Since the benchmark for rating dummies is the group of companies wh rating lower than B, the coefficients of rating dummies are expected to be negative. While the coefficient of none of the industrial classification dummies is significant by self, the differences between some industries are significant. Manufacturing and Public Utilies industries were significantly less risky than firms from Mining & Construction and Wholesale & Retail wh the same rating and firm characteristics. The coefficients of the rating dummy variables are significant, as well as the difference between some coefficients. This is not general proof of the dominance of ratings over publicly available information in prediction of default, but implies that the rating classification had a value added in prediction of default compared to the model based only on the other variables included in the estimation. The coefficients of the dummy variables for the year of issue have the same signs as well as close values to the coefficients in the first run. If these dummy variables represent the macroeconomic suation at the date of rating, can be concluded that ratings do not fully reflect the business cycles. This interpretation fs S&P rating methodology that ratings are assigned to reflect looking through the cycle. The results show that signs of coefficients of most firm specific variables are as in the first run. Coefficient of Secured is negative and significant meaning that the rating does not fully incorporate the signaling of collateral provision. However the other firm-specific 17 In the case of secured debt, rating is notched up. Therefore if two debts have equal ratings but one is secured and the other is not, the issuer of the secured debt has to have a lower rating compared to the other issuer. Therefore in such a case the coefficient of the dummy variable that indicates availabily of collateral should be posive. Note that the signaling affect should already be included in the rating classification and therefore the third run s coefficients should be posive. 25

26 coefficients are insignificant. For instance, the coefficients of Size and Profabily are negative as in the first run but they are not significant. It should also be noted that is possible that the coefficients of these specific variables were insignificant due to the broad definion of the industries and varying parameters. One cricism of ratings is that they cannot fully capture the varying affect of firm-specific variables across industries. For example, two firms wh the same level of leverage but from two different industries might have different level of risk for two reasons. One source of the variation is the difference in the general risk of the two industries and the other is the different effect of leverage on risk in these two industries. Now consider a sample of firms from two different industries in the case that leverage is not correlated wh industry. Once the industrial classification variable is omted, the standard coefficient of the variable Leverage would be biased and larger than the true value (a typical result of omted variables). Therefore, might be that the coefficients of the firm specific variables were insignificant due to the fact that the industrial classifications were too broad. Table IX reports the results in the case where industrial classification is tighter. In these regressions the industries Mining & Construction and Wholesale & Retail as well as Services (omted dummy variable) are classified according to one dig SIC, while Manufacturing and Public & Utilies are sub-classified according to two-dig SIC. Now the third run, which includes all variables, shows that the coefficients of firm-specific variables become more significant and the coefficient of Leverage is already significant. This result suggests that the ratings are indeed not a sufficient statistic for some publicly available information. Furthermore, this disabily might be a result of the fact that the rating did not fully capture the industry-based varying interpretation of these variables. Insert Table IX about here Table X shows the t statistics for the differences between pairs of industries. It appears that, after controlling for rating, some industries did indeed tend to default more than others. For 26